2. Discrete Event Simulation

2.1 Modeling and Simulation

Figure 1 shows a conceptual framework for the modeling and simulation enterprise. The real system, regarded as a source of behavioral data, is some part of the real world of interest. The model is a set of instructions for generating behavioral data of the form of plots of X(variable of interest) against T(time). The modeling relation, linking real system and model, concerns how well the model represents the system. The simulator exercises the model's instructions to generate its behavior. The simulation relation, which links model and simulator, concerns how faithfully the simulator can carry out the instructions of the model.

Figure 1 Modeling and simulation enterprise

2.2 The Types of Mathematical Models

There are several types of mathematical models in terms of time and states shown in Table 2. A continuous state variable changes over continuous time in continuous models, while discrete state variables range over discrete time in digital models. Continuous models are represented through sets of differential equations, and discrete time models through sets of difference equations. Qualitative models are continuous time models in which dependent variables are discretized. Sampled data models use continuous state variables over discrete time. Digital models can be represented through finite state machines.

Discrete event models which use continuous state and continuous time axis differ from continuous models by the fact that only a finite number of state changes may occur within finite time interval depending on instantaneous "events".

Characteristics Types of models	Mathematical Formalism and Application Area	Time	States
Continuous Models	Differential Equation Analog Circuits	Continuous	Continuous
Discrete Event Models	DEVS Formalism Distributed Systems	Continuous	Continuous
Sampled Data Models	Difference Equations Digital Signal Processing	Discrete	Continuous
Qualitative Models	Aritificial Intelligence	Continuous	Symbolic
Digital Models	State Machine Digital Circuits	Discrete	Discrete

Table 1 Mathematical models in terms of time and states

2.3 Discrete Event System

An event is usually a specific action such as customer arrival, a system going down, a stone hitting a window. Events occur instantaneously, and cause transitions from one state to another. The discrete event system is driven by events, and a typical example of discrete system is a queueing system shown as Figure 2.

Customers come in the queue randomly through an input port, and go out to an output port after the amount of time delayed in the queue. The state which is the number of customers in the queue will be changed by incoming customers(input events) or outgoing customers(output event). The behavior of a state transition function is to just add one when a customer comes in (the external transition function in DEVS-C++), or to delete one when a customer goes out from the system (the output and internal transition functions in DEVS-C++).